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Quadratics - Coggle Diagram
Quadratics
Quadratic Functions and Graphics
Function form
Graph Shape : Parabola
Vertex (turning point)
a > 0: Minimum point (U-shaped)
a < 0: Maximum point (n-shaped
Vertex Coordinates
Key Sketch Features: Shape, Axis intercepts, Vertex
Line of Symmetry
Solving Quadratic Equation
Methods
Factorisation
Completing the Square
Quadratic Formula
Quadratic equations in other function (subtitution)
Quadratic inequalitites
solve by sketching graph
Reverse inequality sign if multiplying/dividing by negative
Completing the Square
Quadratic equation
Use completed square form
Standard forms
Completing the square form
Vertex form
The Discriminant
Use the Discriminant Form
Nature of Roots
Δ > 0: Two distinct real roots
Δ = 0: Two equal real roots (one repeated root)
Δ < 0: No real roots
Condition of real roots
Simultaneous Equations (Linear & Quadratic)
Solve by subtitution
Solutions correspond to points of intersection of graphs
Intersection of Line and Curve
Solve simultaneously
Intersection Situations (using Discriminant)
Δ > 0: Two distinct points of intersection
Δ = 0: One point of intersection (Tangent
t Δ < 0: No points of intersection